In mathematics, a supersingular prime is a certain kind of prime number. History Main article: History of mathematics In addition to recognizing how to count concrete objects, prehistoric peoples also recognized how to count abstract quantities, like time -- days, seasons, years. ... In mathematics, a prime number, or prime for short, is a natural number greater than one and whose only distinct positive divisors are one and itself. ...

Formally, let H denote the upper half plane. For a natural number n, let Γ₀(n) denote the modular group Gamma0, and let w_n be the Fricke involution defined by the block matrix [[0, -1], [n, 0]]. Furthermore, let the modular curve X₀(n) be the compactification (with added cusps) of In mathematics, the upper half plane H is the set of complex numbers x + iy such that y > 0. ... Natural number can mean either a positive integer (1, 2, 3, 4, ...) or a non-negative integer (0, 1, 2, 3, 4, ...). Natural numbers have two main purposes: they can be used for counting (there are 3 apples on the table), or they can be used for ordering (this is... In mathematics, a congruence subgroup of a matrix group with integer entries is a subgroup defined by congruence conditions on the entries. ... In mathematics, a modular curve is a Riemann surface, or corresponding algebraic curve, constructed as H/Γ where H is the upper half-plane in the complex numbers, and Γ is a Fuchsian group acting on H, with Γ a subgroup of the modular group of integral 2×2 matrices. ... In mathematics, compactification is applied to topological spaces to make them compact spaces. ... A cusp is a sharp point or apex, such as occurs in two dimensions at the end of a crescent, or in three dimensions at the tip of a cone or horn. ...

Y₀(n) = Γ₀(n)H,

and for any prime p, define

X₀⁺(p) = X₀(p) / w_p.

Then p is supersingular means by definition that the genus of X₀⁺(p) is zero. In mathematics, the genus has few different meanings Topology The genus of a connected, oriented surface is an integer representing the maximum number of cuttings along closed simple curves without rendering the resultant manifold disconnected. ...

It is also possible to define supersingular primes in a number-theoretic way using supersingular elliptic curves defined over the algebraic closure of the finite field GF(p) that have their j-invariant in GF(p). [details, anyone?] Traditionally, number theory is that branch of pure mathematics concerned with the properties of integers. ... In mathematics, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed. ... In mathematics, the j-invariant, regarded as a function of a complex variable τ, is a modular function defined on the upper half plane of complex numbers with positive imaginary part. ...

As is turns out, there are exactly fifteen supersingular primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, and 71 (sequence A002267 in OEIS). It can also be shown that the supersingular primes are exactly the prime factors of the group order of the Monster group M. 2 (two) is the natural number following 1 and preceding 3. ... 3 (three) is a number, numeral, and glyph. ... 5 (five) is the natural number following 4 and preceding 6. ... 7 (seven) is the natural number following 6 and preceding 8. ... 11 (eleven) is the natural number following 10 and preceding 12. ... 13 (Thirteen) is the natural number following 12 and preceding 14. ... 17 (seventeen) is the natural number following 16 and preceding 18. ... 19 (nineteen) is the natural number following 18 and preceding 20. ... 23 (twenty-three) is the natural number following 22 and preceding 24. ... 29 (twenty-nine) is the natural number following 28 and preceding 30. ... 31 is the natural number following 30 and preceding 32. ... 41 is the natural number following 40 and preceding 42. ... 47 is the natural number following 46 and followed by 48. ... 59 is the natural number following 58 and preceding 60. ... 71 is the natural number following 70 and preceding 72. ... The On-Line Encyclopedia of Integer Sequences (OEIS) is a web-based searchable database of integer sequences. ... In mathematics, the Monster group M is a group of order    246 · 320 · 59 · 76 · 112 · 133 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71 = 808017424794512875886459904961710757005754368000000000 ≈ 8 · 1053. ...